The nomination comes one day after Andy Puzder, Trump's first pick to lead the department, withdrew his nomination.

Trump said that Acosta "has been through Senate confirmation three times, confirmed." The comment was an apparent reference to his administration's struggle to get all of their nominees through the Senate.

"I have wished him the best, we just spoke and he is going to be a tremendous secretary of labor," Trump said. Acosta -- the son of Cuban immigrants -- was not at the event with the President.

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Acosta, who is currently the dean of the Florida International University School of Law, is a former member of the National Labor Relations Board, a position he was nominated to by former President George W. Bush.

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Puzder, the CEO of the company that owns the Hardee's and Carl's Jr. fast food chains, faced fierce opposition mostly from Democrats in part related to his position on labor issues as well as the fact that he employed an undocumented immigrant housekeeper.

But Republicans, too, had grown weary of the range of liabilities facing Puzder, and senior GOP officials informed the White House Tuesday night and Wednesday that Puzder lacked a viable path for confirmation.

The turbulent nomination process wore on Puzder, too, with aides close to the nominee telling CNN that he was taken aback by the harshness of politics.